Pseudo-random number generation

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C++ Standard Library
Language Utilities library Strings library Containers library Algorithms library Iterators library Numerics library Input/output library Localizations library Regular expressions library (C++11) Atomic operations library (C++11) Thread support library (C++11)
Numerics library
Common mathematical functions Floating-point environment Complex numbers Numeric arrays Pseudo-random number generation Generic numeric operations iota (C++11) accumulate inner_product adjacent_difference partial_sum
Pseudo-random number generation
Engines and engine adaptors linear_congruential_engine (C++11) mersenne_twister_engine (C++11) subtract_with_carry_engine (C++11) discard_block_engine (C++11) independent_bits_engine (C++11) shuffle_order_engine (C++11) Generators minstd_rand0 minstd_rand mt19937 mt19937_64 ranlux24_base ranlux48_base ranlux24 ranlux48 knuth_b default_random_engine random_device (C++11) Distributions uniform_int_distribution (C++11) uniform_real_distribution (C++11) generate_canonical (C++11) bernoulli_distribution (C++11) binomial_distribution (C++11) negative_binomial_distribution (C++11) geometric_distribution (C++11) poisson_distribution (C++11) exponential_distribution (C++11) gamma_distribution (C++11) weibull_distribution (C++11) extreme_value_distribution (C++11) normal_distribution (C++11) lognormal_distribution (C++11) chi_squared_distribution (C++11) cauchy_distribution (C++11) fisher_f_distribution (C++11) student_t_distribution (C++11) discrete_distribution (C++11) piecewise_constant_distribution (C++11) piecewise_linear_distribution (C++11) Seed Sequences seed_seq (C++11) C library rand srand RAND_MAX

Contents 1 Random number engines 2 Random number engine adaptors 3 Predefined random number generators 4 Random number distributions 4.1 Uniform distributions 4.2 Bernoulli distributions 4.3 Poisson distributions 4.4 Normal distributions 4.5 Sampling distributions 5 Predefined seed sequence generators 6 C library

[edit] Random number engines

Random number engines generate pseudo-random numbers using seed data as entropy source. Several different classes of pseudo-random number generation algorithms are implemented as templates that can be customized.

Defined in header <random>
linear_congruential_engine (C++11)	implements linear congruential algorithm (class template)
mersenne_twister_engine (C++11)	implements Mersenne twister algorithm (class template)
subtract_with_carry_engine (C++11)	implements subtract with carry (a lagged Fibonacci) algorithm (class template)

[edit] Random number engine adaptors

Random number engine adaptors generate pseudo-random numbers using another random number engine as entropy source.

Defined in header <random>
discard_block_engine (C++11)	discards some output of a random number engine (class template)
independent_bits_engine (C++11)	packs the output of a random number engine into blocks of specified number of bits (class template)
shuffle_order_engine (C++11)	delivers the output of a random number engine in different order (class template)

[edit] Predefined random number generators

Several specific popular algorithms are predefined.

Defined in header <random>
Type	Definition
minstd_rand0	linear_congruential_engine<uint_fast32_t, 16807, 0, 2147483647>
minstd_rand	linear_congruential_engine<uint_fast32_t, 48271, 0, 2147483647>
mt19937	mersenne_twister_engine<uint_fast32_t, 32, 624, 397, 31,                         0x9908b0df, 11,                         0xffffffff, 7,                         0x9d2c5680, 15,                         0xefc60000, 18, 1812433253>
mt19937_64	mersenne_twister_engine<uint_fast64_t, 64, 312, 156, 31,                         0xb5026f5aa96619e9, 29,                         0x5555555555555555, 17,                         0x71d67fffeda60000, 37,                         0xfff7eee000000000, 43, 6364136223846793005>
ranlux24_base	subtract_with_carry_engine<uint_fast32_t, 24, 10, 24>
ranlux48_base	subtract_with_carry_engine<uint_fast64_t, 48, 5, 12>
ranlux24	discard_block_engine<ranlux24_base, 223, 23>
ranlux48	discard_block_engine<ranlux48_base, 389, 11>
knuth_b	shuffle_order_engine<minstd_rand0, 256>
default_random_engine	implementation-defined

random_device	non-deterministic random number generator using hardware entropy source (class)

[edit] Random number distributions

Random number distributions are post-process the output of an random number engine or adaptors in such a way, that resulting output fits into some statistical probability distribution.

Defined in header <random>
Uniform distributions
uniform_int_distribution (C++11)	evenly distributes integer random numbers across a range (class template)
uniform_real_distribution (C++11)	evenly distributes floating-point random numbers across a range (class template)
generate_canonical (C++11)	evenly distributes floating-point random numbers of given precision across [0, 1) (function template)
Bernoulli distributions
bernoulli_distribution (C++11)	Produces bool values on a Bernoulli distribution. (class)
binomial_distribution (C++11)	Produces integer values on a binomial distribution. (class template)
negative_binomial_distribution (C++11)	Produces integer values on a negative binomial distribution. (class template)
geometric_distribution (C++11)	Produces integer values on a geometric distribution. (class template)
Poisson distributions
poisson_distribution (C++11)	Produces integer values on a poisson distribution. (class template)
exponential_distribution (C++11)	Produces real values on an exponential distribution. (class template)
gamma_distribution (C++11)	Produces real values on an gamma distribution. (class template)
weibull_distribution (C++11)	Produces real values on a Weibull distribution. (class template)
extreme_value_distribution (C++11)	Produces real values on an extreme value distribution. (class template)
Normal distributions
normal_distribution (C++11)	Produces real values on a standard normal (Gaussian) distribution. (class template)
lognormal_distribution (C++11)	Produces real values on a lognormal distribution. (class template)
chi_squared_distribution (C++11)	Produces real values on a chi-squared distribution. (class template)
cauchy_distribution (C++11)	Produces real values on a Cauchy distribution. (class template)
fisher_f_distribution (C++11)	Produces real values on a Fisher's F-distribution. (class template)
student_t_distribution (C++11)	Produces real values on a Student's t-distribution. (class template)
Sampling distributions
discrete_distribution (C++11)	Produces random integers on a discrete distribution. (class template)
piecewise_constant_distribution (C++11)	Produces real values distributed on constant subintervals. (class template)
piecewise_linear_distribution (C++11)	Produces real values distributed on defined subintervals. (class template)

[edit] Predefined seed sequence generators

Defined in header <random>
seed_seq (C++11)	general-purpose bias-eliminating scrambled seed sequence generator (class)

[edit] C library

Defined in header <cstdlib>
rand	generates a pseudo-random number (function)
srand	initializes pseudo-random number generator (function)
RAND_MAX	maximum possible value generated by rand() (macro constant)